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Entropy
Volume 21
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10.3390/e21020128
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Article

Characterizing Complex Networks Using Entropy-Degree Diagrams: Unveiling Changes in Functional Brain Connectivity Induced by Ayahuasca

by
Aline Viol
1,2,*,
Fernanda Palhano-Fontes
3,
Heloisa Onias
3,
Draulio B. de Araujo
3,
Philipp Hövel
1,2,4 and
Gandhi M. Viswanathan
5,6
1
Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
2
Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany
3
Brain Institute, Universidade Federal do Rio Grande do Norte, Natal–RN 59078-970, Brazil
4
School of Mathematical Sciences, University College Cork, Western Road, T12 XF62 Cork, Ireland
5
Department of Physics, Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil
6
National Institute of Science and Technology of Complex Systems Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(2), 128; https://doi.org/10.3390/e21020128
Submission received: 21 December 2018 / Revised: 13 January 2019 / Accepted: 30 January 2019 / Published: 30 January 2019
(This article belongs to the Special Issue Information Theory in Complex Systems)
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Abstract

With the aim of further advancing the understanding of the human brain’s functional connectivity, we propose a network metric which we term the geodesic entropy. This metric quantifies the Shannon entropy of the distance distribution to a specific node from all other nodes. It allows to characterize the influence exerted on a specific node considering statistics of the overall network structure. The measurement and characterization of this structural information has the potential to greatly improve our understanding of sustained activity and other emergent behaviors in networks. We apply this method to study how the psychedelic infusion Ayahuasca affects the functional connectivity of the human brain in resting state. We show that the geodesic entropy is able to differentiate functional networks of the human brain associated with two different states of consciousness in the awaking resting state: (i) the ordinary state and (ii) a state altered by ingestion of the Ayahuasca. The functional brain networks from subjects in the altered state have, on average, a larger geodesic entropy compared to the ordinary state. Finally, we discuss why the geodesic entropy may bring even further valuable insights into the study of the human brain and other empirical networks.
Keywords: entropy; functional brain networks; psychedelic state; Ayahuasca; complex networks entropy; functional brain networks; psychedelic state; Ayahuasca; complex networks

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MDPI and ACS Style

Viol, A.; Palhano-Fontes, F.; Onias, H.; de Araujo, D.B.; Hövel, P.; Viswanathan, G.M. Characterizing Complex Networks Using Entropy-Degree Diagrams: Unveiling Changes in Functional Brain Connectivity Induced by Ayahuasca. Entropy 2019, 21, 128. https://doi.org/10.3390/e21020128

AMA Style

Viol A, Palhano-Fontes F, Onias H, de Araujo DB, Hövel P, Viswanathan GM. Characterizing Complex Networks Using Entropy-Degree Diagrams: Unveiling Changes in Functional Brain Connectivity Induced by Ayahuasca. Entropy. 2019; 21(2):128. https://doi.org/10.3390/e21020128

Chicago/Turabian Style

Viol, Aline, Fernanda Palhano-Fontes, Heloisa Onias, Draulio B. de Araujo, Philipp Hövel, and Gandhi M. Viswanathan. 2019. "Characterizing Complex Networks Using Entropy-Degree Diagrams: Unveiling Changes in Functional Brain Connectivity Induced by Ayahuasca" Entropy 21, no. 2: 128. https://doi.org/10.3390/e21020128

APA Style

Viol, A., Palhano-Fontes, F., Onias, H., de Araujo, D. B., Hövel, P., & Viswanathan, G. M. (2019). Characterizing Complex Networks Using Entropy-Degree Diagrams: Unveiling Changes in Functional Brain Connectivity Induced by Ayahuasca. Entropy, 21(2), 128. https://doi.org/10.3390/e21020128

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